# R&D Blog

# Normalized Linear Regression Slope | Trading Strategy (Entry)

## I. Trading Strategy

**Concept:** Trend-following strategy based on a normalized linear regression slope. **Source:** Linear Regression Model: Kaufman, P. J. (2005). *New Trading Systems and Methods.* New Jersey: John Wiley & Sons, Inc. ** Research Goal:** Performance verification of the linear regression model. **Specification:** Table 1. **Results:** Figure 1-2. **Portfolio:** 42 futures markets from four major market sectors (commodities, currencies, interest rates, and equity indexes). **Data:** 33 years since 1980. **Testing Platform:** MATLAB®.

## II. Sensitivity Test

All 3-D charts are followed by 2-D contour charts for Profit Factor, Sharpe Ratio, Ulcer Performance Index, CAGR, Maximum Drawdown, Percent Profitable Trades, and Avg. Win / Avg. Loss Ratio. The final picture shows sensitivity of Equity Curve.

Tested Variables: Look_Back & Growth_Index (Definitions: Table 1):

**Figure 1**| Portfolio Performance (Inputs: Table 1; Commission & Slippage: $0).

STRATEGY | SPECIFICATION | PARAMETERS |

Auxiliary Variables: | Linear Regression Slope (LRS) is the slope (angle) of a straight line found using a least-squares regression: LRS = ∑[(X _{i} − AvgX)(Y_{i} − AvgY)] / ∑(X_{i} − AvgX)^{2}where: Y is the price dimension (close prices), X is the time dimension, AvgX is the average value of X_{i} and AvgY is the average value of Y_{i} .Normalized Linear Regression Slope (NLRS) is a linear regression slope normalized by volatility: NLRS = LRS / ATR(ATR_Length) where: ATR (ATR_Length) is the Average True Range over a period of ATR_Length. | Look_Back = [20, 200], Step = 5; ATR_Length = 20; |

Setup: | N/A | |

Filter: | N/A | |

Entry: | Long Trades: A buy at the open is placed when NLRS[i – 1] > Growth_Index. Short Trades: A sell at the open is placed when NLRS[i – 1] < − Growth_Index. Index: i ~ Current Bar. | Growth_Index = [0.0, 0.1], Step = 0.0025; |

Exit: | NLRS Exit: Long Trades: A sell at the open is placed when NLRS[i – 1] < 0. Short Trades: A buy at the open is placed when NLRS[i – 1] > 0.Index: i ~ Current Bar. Stop Loss Exit: ATR(ATR_Length) is the Average True Range over a period of ATR_Length. ATR_Stop is a multiple of ATR(ATR_Length). Long Trades: A sell stop is placed at [Entry − ATR(ATR_Length) * ATR_Stop]. Short Trades: A buy stop is placed at [Entry + ATR(ATR_Length) * ATR_Stop]. | ATR_Length = 20; ATR_Stop = 6; |

Sensitivity Test: | Look_Back = [20, 200], Step = 5 Growth_Index = [0.0, 0.1], Step = 0.0025 | |

Position Sizing: | Initial_Capital = $1,000,000 Fixed_Fractional = 1% Portfolio = 42 US Futures ATR_Stop = 6 (ATR ~ Average True Range) ATR_Length = 20 | |

Data: | 42 futures markets; 33 years (1980/01/01−2013/09/30) |

**Table 1** | Specification: Trading Strategy.

## III. Sensitivity Test with Commission & Slippage

Tested Variables: Look_Back & Growth_Index (Definitions: Table 1):

**Figure 2**| Portfolio Performance (Inputs: Table 1; Commission & Slippage: $100 Round Turn).

## IV. Rating: Normalized Linear Regression Slope | Trading Strategy

A/B/**C**/D

**Related Entries:** Linear Regression Slope (Filter & Entry) | Keltner Channels – 3-Phase Model (Setup) | Combined Donchian Channels (Entry & Exit) | Multiple Time Frames – Bruce Babcock (Entry)

**Related Topics:** (Public) Trading Strategies

**CFTC RULE 4.41:** HYPOTHETICAL OR SIMULATED PERFORMANCE RESULTS HAVE CERTAIN LIMITATIONS. UNLIKE AN ACTUAL PERFORMANCE RECORD, SIMULATED RESULTS DO NOT REPRESENT ACTUAL TRADING. ALSO, SINCE THE TRADES HAVE NOT BEEN EXECUTED, THE RESULTS MAY HAVE UNDER-OR-OVER COMPENSATED FOR THE IMPACT, IF ANY, OF CERTAIN MARKET FACTORS, SUCH AS LACK OF LIQUIDITY. SIMULATED TRADING PROGRAMS IN GENERAL ARE ALSO SUBJECT TO THE FACT THAT THEY ARE DESIGNED WITH THE BENEFIT OF HINDSIGHT. NO REPRESENTATION IS BEING MADE THAT ANY ACCOUNT WILL OR IS LIKELY TO ACHIEVE PROFIT OR LOSSES SIMILAR TO THOSE SHOWN.

**RISK DISCLOSURE: **U.S. GOVERNMENT REQUIRED DISCLAIMER | CFTC RULE 4.41

Codes: matlab/kaufman/linreg-norm/